Adaptive control of an item inventory plan

Abstract

Techniques for determining a decision to acquire units of an item to be inventoried may be provided. For example, a demand for an item may be simulated to determine a consumption of a capacity for inventorying the item. A discrepancy between the consumption of the capacity and the capacity may be determined. An opportunity cost associated with the capacity may be updated based at least in part on determining that the discrepancy fails a convergence criterion. The opportunity cost may indicate a value associated with using the capacity. The consumption of the capacity may be simulated based at least in part on the updated opportunity cost. A resulting discrepancy may be determined. If the resulting discrepancy meets the convergence criterion, the decision to acquire the units of the item may be generated based at least in part on the updated opportunity cost.

What is claimed is: 
     
       1. A computer-implemented method comprising:
 determining, by a computer system, an opportunity cost over a plurality of time periods for using a capacity to store a particular item of a plurality of items of a same category, the capacity associated with inventorying the plurality of items of the same category offered at an electronic marketplace and comprising a receipt capacity for receiving the items in an inventory associated with the electronic marketplace and a storage capacity for storing the items in the inventory, and the opportunity cost determined based at least in part on lost sales of other items of the plurality of items of the same category; 
 simulating, by the computer system, a consumption of the capacity in association with a demand for the particular item from the items based at least in part on the opportunity cost to store the particular item and a set of parameters comprising a merchant capacity of a merchant to provide the particular item, the simulated consumption associated with an initial time period of the plurality of time periods and accounting for the opportunity cost over the plurality of time periods; 
 detecting, by the computer system, that a discrepancy between the simulated consumption and the capacity fails a convergence criterion; 
 updating, by the computer system, the opportunity cost to an updated opportunity cost based at least in part on the discrepancy failing the convergence criterion; 
 re-simulating, by the computer system, the consumption based at least in part on the updated opportunity cost and the set of parameters; 
 detecting, by the computer system, that an updated discrepancy between the re-simulated consumption and the capacity satisfies the convergence criterion; and 
 generating, by the computer system in response to the convergence criterion being satisfied, a decision to add units of the item to the inventory during the initial time period based at least in part on the updated opportunity cost. 
 
     
     
       2. The computer-implemented method of  claim 1 , wherein accessing the opportunity cost comprises initializing the opportunity cost based at least in part on a previous opportunity cost associated with a plurality of previous time periods and setting the initialized opportunity cost as a parameter for simulating the consumption. 
     
     
       3. The computer-implemented method of  claim 1 , wherein the merchant capacity is associated with the initial time period, and wherein the merchant capacity is determined based at least in part on a past performance associated with inventorying items from the merchant during a corresponding past time period relative to past performances corresponding to a plurality of past time periods. 
     
     
       4. The computer-implemented method of  claim 1 , wherein the discrepancy indicates an over-use of the capacity, and wherein updating the opportunity cost comprises increasing the opportunity cost based at least in part the over-use. 
     
     
       5. One or more computer-readable storage media storing computer-executable instructions that, when executed by one or more computing systems, configure the one or more computing systems to perform operations comprising:
 detecting a discrepancy between a consumption of a capacity and the capacity, the consumption determined based at least in part on a simulated demand for an item, the capacity associated with inventorying items of a same category; 
 determining an opportunity cost for using the capacity to store the item, the opportunity cost determined based at least in part on lost sales of other items of the items of the same category; 
 updating the opportunity cost associated with the capacity to an updated opportunity cost based at least in part on determining that the discrepancy fails a convergence criterion, the opportunity cost indicative of a value associated with using the capacity for inventorying the items; 
 simulating the consumption based at least in part on a set of parameters comprising the updated opportunity cost and a merchant capacity to provide the item; 
 detecting that a resulting discrepancy between the simulated consumption and the capacity meets the convergence criterion; and 
 generating a decision to acquire units of the item based at least in part on the updated opportunity cost. 
 
     
     
       6. The one or more computer-readable storage media of  claim 5 , wherein the opportunity cost is associated with a category of items comprising the item, wherein the consumption is associated with simulated demand for the item, wherein simulating the consumption comprises optimizing an objective function based at least in part on an inventory level for the item, and wherein updating the opportunity cost is based at least in part on the inventory level of the item. 
     
     
       7. The one or more computer-readable storage media of  claim 5 , wherein simulating the consumption comprises using an objective function based at least in part on the set of parameters. 
     
     
       8. The one or more computer-readable storage media of  claim 7 , wherein using the objective function comprises optimizing the objective function based at least in part on Lagrange multipliers associated with the opportunity cost. 
     
     
       9. The one or more computer-readable storage media of  claim 8 , wherein an optimal inventory level for the item is determined based at least in part on the Lagrange multipliers. 
     
     
       10. The one or more computer-readable storage media of  claim 7 , wherein using the objective function comprises optimizing the objective function for at least one parameter of the set of parameters, wherein the at least one parameter comprises a profit, wherein optimizing the objective function comprises determining an optimal inventory level for the item that maximizes the profit based at least in part on iteratively setting an inventory level for the item, simulating the demand for the item, and determining the profit. 
     
     
       11. The one or more computer-readable storage media of  claim 10 , wherein the consumption of the capacity is determined based at least in part on the optimal inventory level, wherein updating the opportunity cost comprises decreasing the opportunity cost if the discrepancy between the consumption and the capacity indicates an under-use of the capacity, and wherein the decreasing of the opportunity cost causes an increase in the optimal inventory level. 
     
     
       12. The one or more computer-readable storage media of  claim 7 , wherein updating the opportunity cost comprises optimizing the objective function based at least in part on a sub-gradient algorithm. 
     
     
       13. The one or more computer-readable storage media of  claim 12 , wherein the opportunity cost is updated based at least in part on at least one of a step-size and a direction determined by the sub-gradient algorithm. 
     
     
       14. A system comprising:
 a memory configured to store computer-executable instructions; and 
 a processor configured to access the memory and execute the computer-executable instructions to collectively at least:
 determine an opportunity cost for using a capacity to store an item; 
 detect a discrepancy between a consumption of the capacity and the capacity, the consumption determined based at least in part on a simulated demand for the item to be inventoried and the opportunity cost, the opportunity cost indicative of a value associated with using the capacity to inventory a category of items comprising the item and determined based at least in part on lost sales of other items of the category of items; 
 update the opportunity cost to an updated opportunity cost based at least in part on the discrepancy; 
 simulate the consumption based at least in part on the updated opportunity cost; 
 determine that the discrepancy satisfies a convergence criterion based at least in part on an update to the consumption based at least in part on simulating the consumption; and 
 in response to the determination that the discrepancy satisfies the convergence criterion, generate a decision to inventory units of the item based at least in part on the updated opportunity cost. 
 
 
     
     
       15. The system of  claim 14 , wherein detecting the discrepancy, updating the opportunity cost, and simulating the consumption are iteratively repeated until the convergence criterion is satisfied. 
     
     
       16. The system of  claim 15 , wherein the convergence criterion is satisfied based at least in part on at least one of: an acceptable range of discrepancies, a direction of the discrepancy between multiple simulations, a scale of change in the discrepancy between the multiple simulations, or a change to an objective function used in the simulate. 
     
     
       17. The system of  claim 15 , wherein simulating the consumption comprises iteratively searching for an inventory level based at least in part on a stochastic approximation using an objective function, wherein the iteratively searching is complete when an inner convergence criterion is met based at least in part on one or more of: a harmonic step-size rule, a McClain step-size rule, a Kesten step-size rule, or a bias-adjusted Kalman filter step-size rule. 
     
     
       18. The system of  claim 14 , wherein the opportunity cost and the capacity are associated with a plurality of time periods and with the category of items, wherein the decision to inventory the units of the item is associated with a particular time period of the plurality of time periods and with the item, and wherein the decision is based at least in part on the capacity over the plurality of time periods and a plurality of items from the category of items. 
     
     
       19. The system of  claim 18 , wherein the plurality of time periods comprises a peak demand time period, and wherein the decision to inventory the units of the item comprises at least one of an early order or a late order of the units based at least in part on the opportunity cost to account for the capacity during the peak demand time period. 
     
     
       20. The system of  claim 19 , wherein the opportunity cost is increased during the peak demand time period relative to the particular time period.